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MathsJEE Main 4 Apr 2026, Shift 2·Q10·MCQ·Moderate

Conic Sections · Parametric point on ellipse

Let P(3cos⁡α,2sin⁡α)P(3\cos\alpha, 2\sin\alpha), α≠0\alpha \neq 0, be a point on the ellipse x29+y24=1\dfrac{x^2}{9} + \dfrac{y^2}{4} = 1, QQ be a point on the circle x2+y2−14x−14y+82=0x^2 + y^2 - 14x - 14y + 82 = 0 and RR be a point on the line x+y=5x + y = 5 such that the centroid of the triangle PQRPQR is (2+cos⁡α,3+23sin⁡α)\left(2 + \cos\alpha, 3 + \dfrac23\sin\alpha\right). Then the sum of the ordinates of all possible points RR is:
  1. (1)6
  2. (2)2
  3. (3)4
  4. (4)8

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